Memory State‐Feedback Control for a Linear System With Time‐Varying Delay Based on the Tuning Matrix Search Algorithm

ABSTRACT A multiple augmented Lyapunov function (MALF) is a function that includes more than one augmented matrix, allowing for a more precise evaluation of the relationships between different states within a system and facilitating the analysis of system stability. However, employing multiple augmented matrices can complicate the process of designing controllers. For this issue, this article proposes a controller synthesis algorithm to address the complexity of controller design resulting from multiple augmentation matrices. First, a memory state‐feedback control criterion with tuning matrices is derived by constructing an MALF. Second, a tuning matrix search algorithm is proposed to provide appropriate tuning matrices for the memory state‐feedback control criterion, leading to the determination of optimal controller gains. Finally, the effectiveness and advantage are verified by simulation of load frequency control for in the power system and control for a linear singular time‐delay system.